Solve the system of linear equations using matrices. x+y+z=3 2x+3y+2z=7 3x-4y+z=4

Question

Solve the system of linear equations using matrices.  x+y+z=3  2x+3y+2z=7  3x-4y+z=4

insonsipthinye · Accepted Answer

Step 1  Given equation  x+y+z=3  2x+3y+2z=7  3x-4y+z=4  in matrix form  A=[1112323−41]  B=[374]  X=[xyz]  we know that  A⋅X=B  So, X=A−1⋅B  Step 2  Now,  X=A−1⋅B  We have to find A−1  Adjoin the identity matrix onto the right of the original matrix, so that you have A on the left side and the identity matrix on the right side. [1112323−41]=[100010001]  now we will apply the elementary row method R2−2R1→R2 (multiply 1 row by 2 and subtract it from 2 row), R3−3R1→R3 (multiply 1 row by 3 and subtract it from 3 row)  [1112−2⋅13−2⋅12−2⋅13−3⋅1−4−3⋅11−3⋅1]=[1000−2⋅11−2⋅00−2⋅00−3⋅10−3⋅01−3⋅0][1110100−7−2]=[100−210−301]  R1−1R2→R1 (multiply 2 row by 1 and subtract it from 1 row), R3+7R2→R3 (multiply 2 row by 7 and add it to 3 row)  [10101000−2]=[3−10−210−1771]  R3−2→R3  (divide the 3 row by -2)  [101010001]=[3−10−2108.5−3.5−0.5]  R1−1R3→R1 (multiply 3 row by 1 and subtract it from 1 row)  [100010001]=[−5.52.50.5−2108.5−3.5−0.5]  A−1=[−5.52.50.5−2108.5−3.5−0.5]  Step 3  Now,  X=A−1⋅B

Jeffrey Jordon · Accepted Answer

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Solve the system of linear equations using matrices. x+y+z=3 2x+3y+2z=7 3x-4y+z=4

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